   Chapter 6, Problem 53GQ

Chapter
Section
Textbook Problem

Complete the following table. Interpretation Introduction

Interpretation: The maximum number of orbitals and number of nodal surfaces through the nucleus of s, p, d and f orbitals should be identified.

Concept introduction:

Nodal surfaces: the surface which passing through nucleus where there is zero chance of finding electrons.

The values of l (azimuthal quantum number) when the principal quantum number is n are from 0 to (n1). Each value of l indicates subshell and for l=0,2 and 3 represents s, d and f subshells.

In a subshell there are (2l+1) number of orbital

Explanation
• Each value of l indicates subshell and for s subshells, l=0. In a subshell there are (2l+1) number of orbital Hence, there is only ((2×0)+1)=1 orbital for s subshells. The s subshell has spherical shape and does not have any sharp boundary where the chance of finding electron is zero. The chance of finding electron is never zero in a s subshell. Therefore, zero nodal surface for s orbital
• Each value of l indicates subshell and for p subshells, l=1. In a subshell there are (2l+1) number of orbital. Hence, there are ((2×1)+1)=3 orbitals for p subshells. For p subshells, l=1 and has dumbbell shape. One nodal surface is passing through the p subshell and thus has two electron density regions. Therefore, 1 nodal surfaces for p orbital.
• Each value of l indicates subshell and for d subshells, l=2. In a subshell there are (2l+1) number of orbital. Hence, there are ((2×2)+1)=5 orbitals for d subshells. For d subshells, l=2

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